1 PPS Mathematics Curriculum Grade 6

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Plainfield Public Schools

Mathematics

Unit Planning Organizer

Grade/Course 6th Grade

Unit of Study Number Fluency and Operations

Pacing 9 weeks, including 2 weeks for review and enrichment

Standards for Mathematical Practices

MP1. Make sense of problems and persevere in solving them. MP2. Reason abstractly and quantitatively. MP3. Construct viable arguments and critique the reasoning of others. MP4. Model with mathematics. MP5. Use appropriate tools strategically. MP6. Attend to precision. MP7. Look for and make use of structure. MP8. Look for and express regularity in repeated reasoning.

2 PPS Mathematics Curriculum Grade 6

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I. Unit Standards

UNIT 1 STANDARDS

5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi.? 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standards algorithm for each operation. 6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities 6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations

3 PPS Mathematics Curriculum Grade 6

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“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

FOCUS STANDARD: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Interpret compute solve

fractions fractions

2 3

“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

FOCUS STANDARD 6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities

Understand ratio 1

“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

FOCUS STANDARD 6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship

Understand Unit rate 1

“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

FOCUS STANDARD 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations

Use Ratio and rate reasoning 2

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“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

ADDITIONAL STANDARD: 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

Divide Numbers (standard algorithm) 2

“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

ADDITIONAL STANDARD: 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standards algorithm for each operation.

Compute decimals 2

“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

ADDITIONAL STANDARD: 6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Find Greatest common factor 2

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“Unwrapped” Skills (students need to be able to do)

“Unwrapped” Concepts (students need to know)

DOK Levels

ADDITIONAL STANDARD: 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Add Subtract

Fractions with unlike denominators

2

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II. Mathematical Standards and Practices………… Explanations and Examples Number and Operations—Fractions (NF)

Use equivalent fractions as a strategy to add and subtract fractions. Standards Students are expected to:

Mathematical Practices Explanations and Examples

5. NF.A.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.MP.2. Reason abstractly and quantitatively.

5.MP.4. Model with mathematics.

5.MP.7. Look for and make use of structure.

Students should apply their understanding of equivalent fractions developed in fourth grade and their ability to rewrite fractions in an equivalent form to find common denominators. They should know that multiplying the denominators will always give a common denominator but may not result in the smallest denominator.

Examples:

●

●

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The Number System (NS) Apply and extend previous understanding of multiplication and division to divide fractions by fractions. Standards Students are expected to:

Mathematical Practices Explanations and Examples

6.NS.A.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Connection: 6-8.RST.7

6.MP.1. Make sense of problems and persevere in solving them.

6.MP.2. Reason abstractly and quantitatively.

6.MP.3. Construct viable arguments and critique the reasoning of others.

6.MP.4. Model with mathematics.

6.MP.7. Look for and make use of structure.

6.MP.8. Look for and express regularity in repeated reasoning

Contexts and visual models can help students to understand quotients of fractions and begin to develop the relationship between multiplication and division. Model development can be facilitated by building from familiar scenarios with whole or friendly number dividends or divisors. Computing quotients of fractions build upon and extends student understandings developed in Grade 5. Students make drawings, model situations with manipulatives, or manipulate computer generated models.

Examples:

● 3 people share pound of chocolate. How much of a pound of chocolate does each person get?

Solution: Each person gets lb. of chocolate.

● Manny has yard of fabric to make book covers. Each book is made from yard of fabric. How many book covers can Manny make? Solution: Manny can make 4 book covers.

Continued on next page

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6.NS.A.1. continued ● Represent in a problem context and draw a model to show your solution.

Context: You are making a recipe that calls for cup of yogurt. You have cup of

yogurt from a snack pack. How much of the recipe can you make?

Explanation of Model:

The first model shows cup. The shaded squares in all three models show cup.

The second model shows cup and also shows cups horizontally.

The third model shows cup moved to fit in only the area shown by of the model.

is the new referent unit (whole) .

3 out of the 4 squares in the portion are shaded. A cup is only of a cup

portion, so you can only make of the recipe.

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The Number System (NS) Compute fluently with multi-digit numbers and find common factors and multiples. Standards Students are expected to:

Mathematical Practices Explanations and Examples

6.NS.B.2. Fluently divide multi-digit numbers using the standard algorithm.

6.MP.2. Reason abstractly and quantitatively.

6.MP.7. Look for and make use of structure.

6.MP.8. Look for and express regularity in repeated reasoning.

Students are expected to fluently and accurately divide multi-digit whole numbers. Divisors can be any number of digits at this grade level.

As students divide they should continue to use their understanding of place value to describe what they are doing. When using the standard algorithm, students’ language should reference place value. For example, when dividing 32 into 8456, as they write a 2 in the quotient they should say, “there are 200 thirty-twos in 8456,” and could write 6400 beneath the 8456 rather than only writing 64.

There are 200 thirty twos in 8456.

200 times 32 is 6400.

8456 minus 6400 is 2056.

There are 60 thirty twos in 2056.

There are 4 thirty twos in 136.

4 times 32 is equal to 128.

Continued on next page

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6.NS.B.2. continued

The remainder is 8. There is not a full thirty two in 8; there is only part of a thirty two in 8.

This can also be written as or . There is ¼ of a thirty two in 8.

8456 = 264 * 32 + 8

6.NS.B.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.MP.2. Reason abstractly and quantitatively.

6.MP.7. Look for and make use of structure.

6.MP.8. Look for and express regularity in repeated reasoning.

The use of estimation strategies supports student understanding of operating on decimals.

Example:

● First, students estimate the sum and then find the exact sum of 14.4 and 8.75. An estimate of the sum might be 14 + 9 or 23. Students may also state if their estimate is low or high. They would expect their answer to be greater than 23. They can use their estimates to self-correct.

Answers of 10.19 or 101.9 indicate that students are not considering the concept of place value when adding (adding tenths to tenths or hundredths to hundredths) whereas answers like 22.125 or 22.79 indicate that students are having difficulty understanding how the four-tenths and seventy-five hundredths fit together to make one whole and 25 hundredths.

Students use the understanding they developed in Grade 5 related to the patterns involved when multiplying and dividing by powers of ten to develop fluency with operations with multi-digit decimals.

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The Number System (NS) Compute fluently with multi-digit numbers and find common factors and multiples. Standards Students are expected to:

Mathematical Practices Explanations and Examples

6.NS.B.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2).

6.MP.7. Look for and make use of structure.

Examples:

● What is the greatest common factor (GCF) of 24 and 36? How can you use factor lists or the prime factorizations to find the GCF?

Solution: 22 3 = 12. Students should be able to explain that both 24 and 36 have 2 factors of 2 and one factor of 3, thus 2 x 2 x 3 is the greatest common factor.)

● What is the least common multiple (LCM) of 12 and 8? How can you use multiple lists or the prime factorizations to find the LCM?

Solution: 23 3 = 24. Students should be able to explain that the least common multiple is the smallest number that is a multiple of 12 and a multiple of 8. To be a multiple of 12, a number must have 2 factors of 2 and one factor of 3 (2 x 2 x 3). To be a multiple of 8, a number must have 3 factors of 2 (2 x 2 x 2). Thus the least common multiple of 12 and 8 must have 3 factors of 2 and one factor of 3 ( 2 x 2 x 2 x 3).

● Rewrite 84 + 28 by using the distributive property. Have you divided by the largest common factor? How do you know?

● Given various pairs of addends using whole numbers from 1-100, students should be able to identify if the two numbers have a common factor. If they do, they identify the common factor and use the distributive property to rewrite the expression. They prove that they are correct by simplifying both expressions.

o 27 + 36 = 9 (3 + 4)

63 = 9 x 7

63 = 63

o 31 + 80

There are no common factors. I know that because 31 is a prime number, it only has 2 factors, 1 and 31. I know that 31 is not a factor of 80 because 2 x 31 is 62 and 3 x 31 is 93.

12 PPS Mathematics Curriculum Grade 6

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Ratios and Proportional Relationships (RP)

Understand ratio concepts and use ratio reasoning to solve problems. Standards Students are expected to:

Mathematical Practices Explanations and Examples

6.RP.A.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

6.MP.2. Reason abstractly and quantitatively.

6.MP.6. Attend to precision.

A ratio is a comparison of two quantities which can be written as

a to b, , or a:b.

A rate is a ratio where two measurements are related to each other. When discussing measurement of different units, the word rate is used rather than ratio. Understanding rate, however, is complicated and there is no universally accepted definition. When using the term rate, contextual understanding is critical. Students need many opportunities to use models to demonstrate the relationships between quantities before they are expected to work with rates numerically.

A comparison of 8 black circles to 4 white circles can be written as the ratio of 8:4 and can be regrouped into 4 black circles to 2 white circles (4:2) and 2 black circles to 1 white circle (2:1).

Students should be able to identify all these ratios and describe them using “For every…, there are …” 6.RP.A.2. Understand the concept of a unit rate a/b associated with a ratio a:b with

b 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)

6.MP.2. Reason abstractly and quantitatively.

6.MP.6. Attend to precision.

A unit rate compares a quantity in terms of one unit of another quantity. Students will often use unit rates to solve missing value problems. Cost per item or distance per time unit are common unit rates, however, students should be able to flexibly use unit rates to name the amount of either quantity in terms of the other quantity. Students will begin to notice that related unit rates are reciprocals as in the first example. It is not intended that this be taught as an algorithm or rule because at this level, students should primarily use reasoning to find these unit rates.

In Grade 6, students are not expected to work with unit rates expressed as complex fractions. Both the numerator and denominator of the original ratio will be whole numbers.

Examples:

● On a bicycle you can travel 20 miles in 4 hours. What are the unit rates in this situation, (the distance you can travel in 1 hour and the amount of time required to travel 1 mile)?

Solution: You can travel 5 miles in 1 hour written as and it takes of an hour to travel

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each mile written as . Students can represent the relationship between 20 miles and 4 hours.

● A simple modeling clay recipe calls for 1 cup corn starch, 2 cups salt, and 2 cups boiling water. How many cups of corn starch are needed to mix with each cup of salt?

Ratios and Proportional Relationships (RP)

Understand ratio concepts and use ratio reasoning to solve problems. Standards Students are expected to:

Mathematical Practices Explanations and Examples

6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot

6.MP.1. Make sense of problems and persevere in solving them.

6.MP.2. Reason abstractly and quantitatively.

6.MP.4. Model with mathematics

6.MP.5. Use appropriate tools strategically.

6.MP.7. Look for and make use of structure.

Examples:

● Using the information in the table, find the number of yards in 24 feet.

Feet 3 6 9 15 24 Yards 1 2 3 5 ?

There are several strategies that students could use to determine the solution to this problem.

o Add quantities from the table to total 24 feet (9 feet and 15 feet); therefore the number of yards must be 8 yards (3 yards and 5 yards).

o Use multiplication to find 24 feet: 1) 3 feet x 8 = 24 feet; therefore 1 yard x 8 = 8 yards, or 2) 6 feet x 4 = 24 feet; therefore 2 yards x 4 = 8 yards.

● Compare the number of black to white circles. If the ratio remains the same, how many

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b. the pairs of values on the coordinate plane. Use tables to compare ratios.

c. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

d. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

e. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

black circles will you have if you have 60 white circles?

Black 4 40 20 60 ? White 3 30 15 45 60

● If 6 is 30% of a value, what is that value? (Solution: 20)

● A credit card company charges 17% interest on any charges not paid at the end of the

month. Make a ratio table to show how much the interest would be for several amounts. If your bill totals $450 for this month, how much interest would you have to pay if you let the balance carry to the next month? Show the relationship on a graph and use the graph to predict the interest charges for a $300 balance.

Charges $1 $50 $100 $200 $450 Interest $0.17 $8.50 $17 $34 ?

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III. Essential Questions …………………………...Corresponding Big Ideas

Essential Questions Corresponding Big Ideas

What are rational numbers and how are

they important and useful?

How are numbers and their opposite represented on a number line? What are some ways of working with rational numbers that make sense? How is a ratio or rate used to compare two quantities or values? How and where are ratios and rates used in the real world? Why is it important to know how to solve for unit rates? What is the connection between a ratio and a fraction? What are similarities and differences between fractions and ratios?

The rational numbers are a set of numbers that includes the whole numbers and

integers as well as numbers that can be written as the quotient of two integers,

a divided by b, where b is not zero. Rational numbers allow us to make sense of

situations that involve numbers that are not whole.

A number and its opposite are at opposite are at equals distances from zero on

a number line

The rational numbers allow us to solve problems that are not possible to solve

with just whole numbers or integers.

Reasoning with ratios involves attending to and coordinating two quantities. A ratio is a multiplicative comparison of two quantities, or it is a joining of two quantities in a composed unit. Forming a ratio as a measure of a real-world attribute involves isolating that attribute from other attributes and understanding the effect of changing each quantity on the attribute of interest. A number of mathematical connections link ratios and fractions: Ratios and fractions can be thought of as overlapping sets. Ratios can often be meaningfully reinterpreted as fractions. Ratios can be meaningfully reinterpreted as quotients. Ratios are often expressed in fraction notation, although ratios and fractions do not have identical meaning. Ratios are often used to make “part-part” comparisons, but fractions are not.

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Source: Lobato, J. E. (2010). Developing essential understanding of ratios, proportions &

proportional reasoning for teaching mathematics in grades 6-8. Reston, VA: The

National Council of Teachers of Mathematics, Inc.

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IV. Student Learning Objectives Student Learning Objectives Skills/Concepts Instructional Clarification

Mathematics Assessment Test

Specification

Mathematical

Practices

Compute quotients of fractions. Construct visual fraction models to represent quotients of fractions and use the relationship between multiplication and division to explain division of fractions. Solve real-world problems involving quotients of fractions and interpret the solutions in the context given. 6.NS.1

Concept(s): No new concept(s) introduced Students are able to:

Divide a fraction by a fraction.

Represent division of fractions using visual models.

Interpret quotients of fractions in the context of the problem.

Compute quotients of fractions in order to solve word problems.

Write equations to solve word problems involving division of fraction by a fraction.

Use the relationship between multiplication and division to explain division of fractions.

Only the answer is required.

Note that the italicized

examples correspond to three meanings/uses of division:

(1) equal sharing (2) measurement; (3) unknown factor. These meanings/uses of division should be sampled equally.

Tasks may involve fractions and mixed numbers but not decimals.

Base arithmetic

explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method.

MP.4

Fluently divide multi-digit numbers using the standard algorithms. 6.NS.2

Concept(s): No new concept(s) introduced Students are able to:

Use the standard algorithm to

● The given dividend and divisor require an efficient/standard algorithm (e.g., 40584 ÷ 76).

● Tasks do not have a

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divide multi-digit numbers with speed and accuracy.

context. ● Only the answer is required. ● Tasks have a maximum of

five-digit dividends and a maximum of two digit divisors.

● Tasks may or may not have a remainder. Students understand that remainders can be written as fractions or decimals

Explain the relationship of two quantities in given ratio using ratio language. 6. RP.A.1

Concept(s): A ratio shows relative sizes or

values of two quantities.

Students are able to:

Describe a ratio relationship between two quantities using ratio language.

Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions.

Expectations for ratios in

this grade are limited to ratios of non-complex fractions. The initial numerator and denominator should be whole numbers.

MP.2

Use rate language, in the context of the ratio relationship, to describe a unit rate. 6. RP.A.2

Concept(s): A rate is a ratio comparing two

different types of quantities.

Students will be able to:

Determine the unit rate given a ratio relationship.

● Expectations for ratios in

this grade are limited to ratios of

non-complex fractions. The initial

numerator and denominator should

be whole numbers.

MP.2

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Describe a unit rate relationship between two quantities using rate language.

Create and complete tables of equivalent ratios to sole real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100. Use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities

Concept(s): No new concept(s) introduced Students are able to:

Use ratio and rate reasoning to create tables of equivalent ratios relating quantities with whole number measurements, find missing values in tables and plot pairs of values.

Compare ratios using tables of equivalent ratios.

Solve real world and mathematical problems involving unit rate (including unit price and constant speed).

Calculate a percent of a quantity and solve problems by finding the whole when given the part and the percent.

Convert measurement units using ratio reasoning.

Transform units appropriately when multiplying and dividing quantities.

.

Expectations for unit rates in this grade are limited to non-complex fractions. The initial numerator and denominator should be whole numbers

MP.2 MP.4 MP.5 MP.6 MP.7 MP.8

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Unit 1 Vocabulary

Unit Vocabulary Terms

greatest common factor (GCF) integers least common multiple (LC M) quotient divisor dividend Less than Greater than Equivalent Increase Decrease

Absolute Value Integers Negative Numbers Positive Numbers Rational Numbers Repeating Decimal Ratio Unit rate Equivalent fraction Improper fraction Mixed numbers inverse

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VI. Differentiations/Modifications for Teaching

Research Based Effective Teaching Strategies

Modifications (how do I differentiate instruction?)

Special Education Strategies for English Language Learners

Task /Activities that solidifies mathematical concepts Use questioning techniques to facilitate learning

Reinforcing Effort, Providing Recognition

Practice, reinforce and connect to other ideas within mathematics

Promotes linguistic and nonlinguistic representations

Cooperative Learning Setting Objectives, Providing Feedback

Varied opportunities for students to communicate mathematically

Use technological and /or physical tools

Modifications Before or after school tutorial program Leveled rubrics Increased intervention Small groups Change in pace Calculators Extended time Alternative assessments Tiered activities/products Color coded notes Use of movements Use any form of technology Extension See Connected Mathematics Program 3 Classroom Differentiation for Gifted Students

Change in pace Calculators Alternative assessments Accommodations as per IEP Modifications as per IEP Use graphic organizer to clarify mathematical functions for students with processing and organizing difficulties’. Constant review of math concepts to strengthen understanding of prior concepts for difficulties recalling facts. Use self-regulations strategies for student to monitor and assess their thinking and performance for difficultly attending to task Cooperative learning (small group, teaming, peer assisted tutoring) to foster communication and strengthen confidence.

Whiteboards Small Group / Triads Word Walls Partially Completed Solution Gestures Native Language Supports Pictures / Photos Partner Work Work Banks Teacher Modeling Math Journals See Connected Mathematics Program 3 for Classroom Differentiation foe English Language Learners

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21st Century Learning Skills:

Teamwork and Collaboration

Initiative and Leadership

Curiosity and Imagination

Innovation and Creativity

Critical thinking and Problem Solving

Flexibility and Adaptability

Effective Oral and Written Communication

Accessing and Analyzing Information

Use technology and/or hands on devices to: clarify abstract concepts and process for: 1. Difficulty interpreting pictures and diagram. 2.difficulties with oral communications 3. Difficulty correctly identifying symbols of numeral 4.Difficulty maintaining attentions Simplify and reduces strategies / Goal structure to enhance motivation, foster independence and self-direction for: 1.difficulty attending to task 2. difficulty with following a sequence of steps to solution. 3.difficulty processing and organizing Scaffolding math idea/concepts guided practice and questioning

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strategies’ to clarify and enhance understanding of math big ideas for: 1.Difficulty with process and organization 2.difficulty with oral and written communication Teacher models strategies’ and think out aloud strategies to specify step by step process for 1. Difficulties processing and organization 2. Difficulty attending to tasks. Use bold numbers and/or words to draw students’ attention to important information. *Prepare on index cards instructions for students to locate points on a number line. Using fingers or technology move to the left or right of the zero to locate path. After reading aloud, encourage students to verbalize or explain the movement on the number line. *Arrange manipulatives or desk into rows and columns representing a coordinate grid system, have student sitting in seats. Call out ordered pairs for desk in the arrangement and ask students to stand when the ordered pair that names their seat is called See Connected Mathematics

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Program 3 Classroom Differentiation for Special Need Students

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Vll. Instructional Resources and Materials

Instructional Resources and Materials

Formative Assessment Print Short constructed responses Extended responses Checks for Understanding Exit tickets Teacher observation Projects Timed Practice Test – Multiple Choice & Open-Ended Questions Performance Tasks:

Traffic Jam aligned to 6.NS.A1

Shirt Sale aligned 6.RP.A.3c

Additional performance Task for

Class use:

6.RP.A.1 Games at Recess 6.RP.A.2 Price per pound and pounds per dollar 6.RP.A.3 Voting for Three, Variation 1 6.RP.A.3c Shirt Sale 6.NS.B.3 Reasoning about Multiplication and Division and Place Value, Part 1 6.NS.B.4 Factors and Common Factors

Connected Math Program Grade 6 Unit: Comparing Bits and Pieces Connected Math Program Grade 6 Scope and Sequence Connected Math Program Grade 6 Unit: Let’s Be Rational Connected Math Program Grade 6 Scope and Sequence

Technology

Resources for teachers

*NJ CORE Connected Math Project ( Michigan State University) My Pearson Training : Connected Math Program Annenberg Learning : Insight into Algebra 1 National Council of Teachers of Mathematics Mathematics Assessment Projects Achieve the Core Illustrative Mathematics Mathematics Assessment Projects Get the Math Webmath.com sosmath.com Mathplanet.com Interactive Mathematics.com Inside Mathmatics.org Asia Pacific Economic Cooperation : :Lesson Study Videos Genderchip.org Interactive Geometry Mathematical Association of America learner.org Math Forum : Teacher Place

Resources for Students My Math Universe.com Math is Fun website Khan Academy Figure This.org website Virtual Nerd website Math Snacks websites Internet 4 Classroom website A Maths Dictionary for kids

26 PPS Mathematics Curriculum Grade 6

Hyperlinks are noted underlined in italics

6.NS.B.4 Multiples and Common Multiples

Project:

Teach 21 Problem Based Learning

: Let's Party